On the nullcone of representations of reductive groups

• Autores: Hanspeter Kraft, Nolan R. Wallach
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 224, Nº 1, 2006, págs. 119-140
• Idioma: inglés
• DOI: 10.2140/pjm.2006.224.119
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• Resumen

  • We study the geometry of the nullcone N = NV ?k for several copies of a representation V of a reductive group G and its behavior for different k. We show that for large k there is a certain ¿stability¿ with respect to the irreducible components. In the case of the so-called ?-representations, this can be made more precise by using the combinatorics of the weight system as a subset of the root system. All this finally allows us to calculate explicitly and in detail a number of important examples, such as the cases of 3- and 4-qubits, which play a fundamental rôle in quantum computing.